In the previous GSM and UMTS system, precisely one core network node is rigidly assigned to an identifiable radio area, i.e. to a location or routing area. In 3GPP, too, a method is specified in which a special routing parameter is assigned to each terminal during the new registration in a core network area which is covered by different core network nodes. In this arrangement, the mobile communications terminal must detect a change of core network area and indicate this to the network. In most cases, this routing parameter is also coded in parallel in the temporary subscriber identity (P-)TMSI and identifies exactly one core network node within a core network area. Such a core network area consists of a number of identifiable radio areas. If the terminal changes the identifiable radio areas but remains within such a core network area, the core network node is not changed. This distribution of terminals to corresponding core network nodes enlarges the total radio area covered by a single core network node. This reduces the signaling load, particularly that with the home location register. Availability is increased by a number of nodes which are operated in parallel. This improves the reliability. In addition, the scalability of the overall system is improved. Moreover, the number of handovers between the core network nodes is reduced. So that it is always the same core network node which serves the terminal within a core network area, the radio system sets up the signaling link for a terminal with the respective core network node in accordance with the routing parameter assigned. If a core network area is changed, the terminal informs the radio system that it is new in this core network area. The terminal recognizes this from the identities of the identifiable radio areas which are provided with a special structure for this purpose. In the case of such a change of the core network area, the radio system selects a new core network node which is to serve the terminal from then on, for example, by a load distribution between the possible core network nodes. The new core network node usually provides the mobile communications terminals with a new routing parameter and a new temporary subscriber identity. These are stored by the mobile communications terminal and sent to the network again during subsequent signaling.